found the pressure of the fluids in the various tubes, by taking into account these several circumstances—the gravitation, with the centrifugal tendencies, the lengths of the different portions of the pipes, and the density of the fluid in each of those portions of the pipes on which the forces are acting; when you have taken these into consideration, you find the pressure of the fluid at the place E where the two pipes meet; then, by the principle of the equality of the pressures of fluids in all directions, you must have the two pressures at E equal, or the fluid will not be in a state of rest. Suppose then, that we have assumed such a degree of ellipticity for the external surface of the earth, and such ellipticities for the different strata, that this condition of equality of pressure at E is satisfied; still we have not done all that is necessary. It is necessary that, if we suppose two or more tubes of any shape whatever, drawn from any points of the surface to any point of the fluid, as for instance, the point K, or the point L, in Figure 62, the pressures at K produced by the fluids in the different tubes abutting at K shall be equal; and similarly, that the pressures at L produced by the fluids in the different tubes abutting at L shall be equal.
These considerations make the problem rather complicated. However, it can be completely solved, whatever be the succession of densities of the different strata; and the result is this. According to the law of density of the successive strata, the law of the ellipticities of the successive strata would be different, and the amount of the ellipticity of the earth's surface would be different. Except you know what is the structure of the interior, you cannot say what the ellipticity of the earth will be; but whatever that law
